Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-9x-3y &= -1 \\ -7x+y &= -3\end{align*}$
Begin by moving the $x$ -term in the second equation to the right side of the equation. $y = {7x-3}$ Substitute this expression for $y$ in the first equation. $-9x-3({7x - 3}) = -1$ $-9x - 21x + 9 = -1$ Simplify by combining terms, then solve for $x$ $-30x + 9 = -1$ $-30x = -10$ $x = \dfrac{1}{3}$ Substitute $\dfrac{1}{3}$ for $x$ back into the top equation. $-9( \dfrac{1}{3})-3y = -1$ $-3-3y = -1$ $-3y = 2$ $y = -\dfrac{2}{3}$ The solution is $\enspace x = \dfrac{1}{3}, \enspace y = -\dfrac{2}{3}$.